Topology Optimization Method of Lattice Structures Based on a Genetic Algorithm

Feng Ruo-qiang,Liu Feng-cheng,Xu Wei-jia,Liu Yang 한국강구조학회 2016 International Journal of Steel Structures Vol.16 No.3

A two-stage topology optimization method of lattice structures based on a genetic algorithm is proposed. The first stage is the form-finding analysis of lattice structures, and the optimal initial shape was achieved with the numerical inverse hanging method. The second stage is the topology optimization of single-layer lattice structures, which can be realized by changing the mesh size and the tube configurations to minimize the total weight of steel tubes subject to the design requirements. The mesh configuration optimization is realized through the adjustment of the nodal horizontal co-ordinates and the removal of tubes with lower stress. The maximum displacement of the structure, the maximum stress of the circular steel tubes, and the nonlinear buckling load are the state variables, and a genetic algorithm (GA) is the optimization algorithm. Different stress-limiting values used to delete the tubes were discussed. The numerical examples show that the two-stage topology optimization method for lattice structures proposed in this paper is correct and efficient. Furthermore, the forms of the optimized structure are rich, and the structure is lightweight and efficient.

Shape Optimization Method of Free-form Cable-braced Grid Shells Based on the Translational Surfaces Technique

Ruo-qiang Feng,Jin-ming Ge 한국강구조학회 2013 International Journal of Steel Structures Vol.13 No.3

Cable-braced grid shells, being a new type of single-layer reticulated shell, are widely used in glass roofs. However, research on the shape optimization of free-form cable-braced grid shells is relatively lacking. This paper describes a shape optimization method for cable-braced free-form grid shells, with strain energy used as the optimization object, structural height used as the optimization variable, and the conjugate gradient method used as the optimization algorithm. According to the shape forming method for grid shells, their shape optimization can be realized only by adjusting the generatrix and directrix, not by optimizing the whole surface. The B-spline curve method is used to model the generatrix and directrix and maintain an optimized surface fairing. The following conclusions can be drawn from this study. First, the structural mechanical behavior of grid shells can be significantly improved with rapid convergence using the proposed shape optimization method. Second, the plane quadrilateral mesh is maintained and fewer optimization variables are needed during the proposed shape optimization method. Finally, the optimized surface is fairing and the mechanical properties of the optimized surface are somewhat decreased when using the B-spline curve method.

Mechanical Behavior of Glass Panels Supported by Clamping Joints in Cable Net Facades

Ruo-qiang Feng,Ji-hong Ye,Yue Wu,Shi-zhao Shen 한국강구조학회 2012 International Journal of Steel Structures Vol.12 No.1

In glass panels supported by clamping joints in a cable net facade, the clamping joint restrains movement at the four corners of the glass panel. As a result, the mechanical behavior of the glass panels supported by clamping joints is very different than the behavior of glass panels supported by four hinged corners. Moreover, the deformation in cable net facade is large and nonuniform; thus, the glass panels in cable net facades bear the effects of warping distortion. In this study, a model test and theoretical analysis was conducted to study the mechanical behavior of glass panels supported by clamping joints in a cable net facade. To this end, a cable net facade was designed, and a proper experimental model was constructed. A static mechanical model test was conducted, where the glass stress at different positions in the cable net was measured. A numerical model of the cable net facade was developed, and the results of the experiment and the numerical analysis were compared. Furthermore,the numerical results provided a detailed description of the mechanical behavior of the glass panels in a cable net facade.

A Mode Contribution Ratio Method for Seismic Analysis of Large-span Spatial Structures

Ruo-qiang Feng,Zhu Baochen,Xin Wang 한국강구조학회 2015 International Journal of Steel Structures Vol.15 No.4

The structural forms of large-span spatial structures can be characterized by the dense distribution of their natural frequencies, and their vibration subjected to seismic loads is three-dimensional. There are many modes that contribute to the seismic response. The high-order modes typically dominate. The mode superposition dynamic analysis method used for seismic design of spatial structures requires a criterion to determine the dominant modes. The criterion for tall buildings is not applicable for spatial structures; instead, we have proposed the mode contribution ratio method for the selection of the dominant modes of spatial structures subjected to seismic loads. A set of 18 typical cases of different single-layer spherical lattice shells was used to verify the validity of this method. The following conclusions can be drawn: First, the method for combining the first thirty modes to calculate the seismic responses specified in the Technical Specification for Space Frame Structures is not accurate and is not applicable to spatial structures. Second, the mode contribution ratio method can be used to choose the dominant modes of spatial structures. Third, the mode contribution ratio is physically different from the effective mass ratio. Especially when the structural mass distribution is uneven, the two ratios are different, and the mode contribution ratio is more precise in calculation of the seismic responses of spatial structures.

Multi-objective Morphology Optimization of Free-form Cable-braced Grid Shells

Ruo-qiang Feng,linlin Zhang,Jin-ming Ge 한국강구조학회 2015 International Journal of Steel Structures Vol.15 No.3

This paper examines the multi-objective morphology optimization of free-form cable-braced grid shells. First, according to the shape forming method for grid shells, shape optimization can be realized by adjusting the generatrix and directrix rather than optimizing the whole surface. Second, the multi-objective shape optimization of free-form cable-braced grid shells is conducted. According to different practical requirements, the mechanical and geometric indexes, mechanical and economic indexes, or different mechanical indexes are used as multiple optimization objectives. Four main conclusions can be drawn from this study. First, with the above shape optimization method, the optimized surface does not change significantly; therefore, this method is useful in the shape optimization of grid shells with given initial surfaces. Second, among the static mechanical performance indexes, the mechanical behavior of the cable-braced grid shell is better with strain energy as the optimization objective. Third, with the weight of steel tubes and strain energy as the optimization objectives, the result of the multi-objective optimization that combines section optimization with shape optimization is favorable and practical in engineering applications. Fourth, when strain energy and the variance of the tube lengths are used as multiple optimization objectives, the structural mechanical behavior is not sensitive to the weight factor of variance of the tube lengths.

Analysis of Wind-Induced Vibration Response of High-Rise Structure of Heat Sink Tower Based on Large Eddy Simulation

Ruo-qiang Feng,Chang-jun Zhong,Jing He 한국강구조학회 2022 International Journal of Steel Structures Vol.22 No.1

Taking the heat absorption tower of Dubai photothermal project as the research object, a three-dimensional fi nite element model of the high-rise structure of the heat absorption tower is established by using large eddy simulation technology and a new generation method of turbulent fl uctuating fl ow fi eld—Random Number Recycling Method. Then the rationality of random number cyclic pre simulation method is analyzed. On this basis, the turbulent boundary conditions of the fl ow fi eld around the heat absorption tower structure are simulated, the wind fl ow fi eld and wind load time history data around the structure are obtained, and the modal analysis and wind vibration response analysis are carried out. In addition, the eff ects of tower top wind speed, wind direction angle and damping ratio on wind-induced vibration response are explored, and the eff ects of cross wind vortex induced vibration and wind break ring on vortex induced vibration are analyzed. The results show that it is reasonable to use the random number cyclic pre simulation method as the inlet boundary condition of large eddy simulation. Secondly, the actual critical wind speed at the top of the tower for vortex induced resonance of the highrise structure of the heat absorption tower is 63 m/s, and the most unfavorable wind angle is 75°. In addition, for this kind of high-rise structure of heat absorption tower, the recommended value range of damping ratio is 0.15–1%. In addition, the setting of wind break ring makes the average decrease of structural displacement and internal force up to 39.3%, which eff ectively reduces the infl uence of cross wind vortex induced resonance.

Simulation of Nonlinear Behavior of Beam Structures Based on Discrete Element Method

Ruo-qiang Feng,Baochen Zhu,Chunchang Hu,Xi Wang 한국강구조학회 2019 International Journal of Steel Structures Vol.19 No.5

In this paper, the discrete element method (DEM) is improved to simulate the strong nonlinear mechanics behavior of beam structures. First, the spring stiff ness of parallel bond model applied to beam structure is deduced using the principle of energy conservation, and the relationship between spring stiff ness and elastic constants is established. Second, the layered beam theory is introduced into the traditional DEM. The yield criteria and the spring stiff ness of contact in yield state are deduced, so that the improved DEM can be used to solve the plastic problem of beam structures. Third, the fracture criterion based on the limit strain of material is defi ned, so that the fracture problem of steel beams can be solved by DEM. Fourth, the force–displacement equations of Hertz model is deduced. Finally, the numerical examples show that the improved DEM can eff ectively solve the problems of large deformation, plasticity, fracture, contact and collision of beam structures.

Shear Performance of Steel Thin Sheet-to-Thick Plate Bolted Connections

Shen Liu,Ruo-qiang Feng,Chang-jun Zhong 한국강구조학회 2023 International Journal of Steel Structures Vol.23 No.4

This paper presents a study on the bolted connections of cold-formed steel (CFS) sheets and hot-rolled steel (HRS) plates. The test strengths and failure modes were compared with the results predicted by the North American Specification (AISI S 100–16) and European Standard (EN1993-1–3) for CFS structures. Additionally, the influence of the fastener diameter and the thickness of the CFS sheets and HRS plates on the specimens were discussed. In addition, numerical modeling of the specimens was established to simulate the failure modes and load-deformation relationships. Finally, a modified equation for bearing strength is proposed, discussed, and verified by reliability analysis. The results showed that bearing failure, shear failure and net section failure were observed. The nominal strengths predicted by AISI S 100 and EN 1993–1-3 are generally conservative. The numerical models can predict the failure modes and load-deformation relationships of the specimens with good agreement. In addition, the proposed method for the bearing strength of the connections has better accuracy than the current specifications.

The Modified Force-Density Method for Form-Finding of Membrane Structures

Jihong Ye,Ruo-qiang Feng,Shulu Zhou,Jun Tian 한국강구조학회 2012 International Journal of Steel Structures Vol.12 No.3

In the force-density method, the value of force-density can only be determined after several trial calculations by now, which often depend on the experience of the researcher. This makes the process of form-finding inefficient and sometimes even invalid. In this manuscript, the disadvantage of the above-mentioned method was overcome through the following two modifications: membrane stress and cable tension were used as initial conditions instead of assuming the value of force-density (i.e. the quantitative relationships between the membrane stress, the cable tension and the force-density are established), and the unbalanced force of each node was used to control the error. This significantly reduced the number of trial calculations required. Several complex cases showing the validity and efficiency of the algorithm. A form-finding experiment of the membrane structure using Fluotop T2 was conducted in order to verify the modified force-density method. The experimental model was a saddle-shaped tensile membrane with 4 cable boundaries, 4 supports and a plane size of 4 m×4 m. The following three parameters were selected for measurement: (a) cable strains, (b) membrane strains and (c) coordinates of several testing points on the membrane surface in two states of the model, one called the unrestrained state and the other called the equilibrium state. These three parameters were compared among the results of the experiment, numerical simulation and analytical methods. We concluded that the modified force-density method was valid and can be used in the form-finding analysis for membrane structure engineering applications.

Effect of Joint Stiffness on the Stability of Cable-braced Grid Shells

Xi Wang,Ruo-qiang Feng,Gui-rong Yan,Feng-cheng Liu,Wei-jia Xu 한국강구조학회 2016 International Journal of Steel Structures Vol.16 No.4

Bolted joints used in cable-braced grid shells are typically semi-rigid joints, and the joint stiffness has a significant effect on the stability of cable-braced grid shells. The effect of joint stiffness on the stability of cable-braced grid shells is studied in this paper. Based on the experimental results of improved bolted joints, finite element models of elliptic paraboloid cable-braced grid shells with bolted joints are established, and spring elements are used to simulate the joint stiffness. The effect of the joint stiffness on the nonlinear buckling load is studied by changing the joint stiffness. The main conclusions are as follows. First, the joint rotational stiffness has a significant effect on the failure mode. When the joint rotational stiffness is small to a certain extent, the failure mode of cable-braced grid shells changes from overall buckling to local buckling. Second, the nonlinear failure mode is similar to the first-order eigenvalue buckling mode and the maximal compression stress distribution. The structural integrity is weakened, and the maximal steel tube compression stress decreases with the decrease of the joint rotational stiffness. The smaller the joint rotational stiffness, the lower the utilization rate of steel strength. The results suggest that the joint stiffness of elliptic paraboloid cable-braced grid shells should not be less than 20% of the rigid joint stiffness.